Error analysis in the reconstruction of a convolution kernel in a semilinear parabolic problem with integral overdetermination

DOI10.1016/j.cam.2014.06.026zbMath1334.65147OpenAlexW1973351647MaRDI QIDQ457756

Marián Slodička, Karel Van Bockstal, Rob H. De Staelen

Publication date: 29 September 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.06.026

zbMATH Keywords

error analysisreconstructionconvolution kernelintegral overdeterminationparabolic IBVP

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (14)

Determination of a time-dependent convolution kernel in a non-linear hyperbolic equation ⋮ Inverse potential problem for a semilinear generalized fractional diffusion equation with spatio-temporal dependent coefficients ⋮ Recovery of a time-dependent heat source in one-dimensional thermoelasticity of type-III ⋮ A multistep collocation method for solving advection equations with delay ⋮ Editorial: Recent trends on computational and mathematical methods in science and engineering (CMMSE) ⋮ Error estimates for the full discretization of a semilinear parabolic problem with an unknown source ⋮ A difference scheme for multidimensional transfer equations with time delay ⋮ Determination of a time-dependent convolution kernel from a boundary measurement in nonlinear Maxwell's equations ⋮ Identification of a memory kernel in a nonlinear integrodifferential parabolic problem ⋮ Determining the memory kernel from a fixed point measurement data for a parabolic equation with memory effect ⋮ Identification of memory kernels in hyperbolic problems ⋮ On a Finite Difference Scheme for an Inverse Integro-Differential Problem Using Semigroup Theory: A Functional Analytic Approach ⋮ Identification of a memory kernel in a semilinear integrodifferential parabolic problem with applications in heat conduction with memory ⋮ First order partial differential equations with time delay and retardation of a state variable

Uses Software

• DOLFIN
• FEniCS

Cites Work

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• Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions
• Convergence to a stationary state for solutions to parabolic inverse problems of reconstruction of convolution kernels.
• Automated solution of differential equations by the finite element method. The FEniCS book
• Determination of an unknown diffusion coefficient in a semilinear parabolic problem
• DOLFIN
• The inverse problem of finding the time-dependent diffusion coefficient of the heat equation from integral overdetermination data
• Inverse problem for a parabolic equation with integral overdetermination
• A GLOBAL IN TIME EXISTENCE AND UNIQUENESS RESULT FOR A SEMILINEAR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEM IN SOBOLEV SPACES

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